Time-resolved Degenerate Four-wave Mixing Research Articles

Biexcitonic nonlinear response in GaAs thin film studied by degenerate four-wave mixing

Nonlinear optical response of a high-quality GaAs thin film of 200 nm thickness was studied by time-resolved degenerate four-wave mixing (DFWM) using pico-second excitation pulses at low temperature (5 K). The DFWM signals show a strong nonlinearity due to biexciton at a slightly lower energy of exciton resonance. The polarization dependence of the DFWM also reveals that higher-order nonlinear response is dominated by biexciton processes.

CCD broadband detection technique for the spectral characterization of the inhomogeneous signal in femtosecond time‐resolved four‐wave mixing spectroscopy

The spectral analysis of the inhomogeneous signal obtained from femtosecond (fs) time-resolved degenerate four-wave mixing spectroscopy on iodine vapor with the help of CCD broadband detection is reported. It is shown with this spectral analysis that the broad band detection technique makes the simultaneous observation of femtosecond time-resolved coherent anti-Stokes Raman scattering (CARS), coherent Stokes Raman scattering (CSRS) and degenerate four-wave mixing (DFWM) processes possible. The fs lasers employed in our studies possess spectral widths which allow not only for a DFWM process but also other forms of four-wave mixing (FWM) processes such as CARS and CSRS to take place simultaneously in the molecular sample. These processes show themselves at different spectral positions within the FWM signal. The separation of the FWM signal with help of a monochromator and subsequent broadband detection with a CCD camera allow all the spectral components of the signal to be detected simultaneously under identical experimental conditions. As a result, the different FWM processes can be compared with one another directly and the continuous transition between these processes can be observed. Furthermore, the high quantum efficiency innate to a CCD camera allows for an evident improvement in the quality of the recorded transient FWM signal in comparison with detection with a fast photomultiplier. Copyright ” 1999 John Wiley & Sons, Ltd.

Femtosecond pump-probe and four-wave mixing spectroscopies applied to simple molecules

A femtosecond three color pump/dump-probe scheme in combination with a time-of-flight (TOF) mass selective detection unit has been applied to study vibrational wave packet dynamics in the electronic ground state of cold K 2 molecules. A spectral analysis of the time domain signal reveals two different wave packet contributions: one from a stimulated Raman process and one from stimulated emission pumping. Also femtosecond time-resolved degenerate four-wave mixing (DFWM) spectroscopy is performed in order to investigate molecular dynamics in iodine molecules in the gas phase. Depending on the timing of the laser pulses different dynamics are reflected in the DFWM transient signal. By the use of time-evolution diagrams, the varying contribution of ground and excited state dynamics can be explained conclusively.

Measurement and theoretical modeling of quantum beats in picosecond time-resolved degenerate four-wave mixing and polarization spectroscopy of OH in atmospheric pressure flames

Using tunable ultraviolet picosecond laser pulses pump-probe degenerate four-wave mixing (DFWM) and polarization spectroscopy experiments were conducted in atmospheric pressure flames to investigate the temporal signal behavior in selected rotational transitions of the OH $A{}^{2}\ensuremath{\Sigma}--X{}^{2}\ensuremath{\Pi} (0,0)$ electronic band. The relaxation behavior of simultaneously excited main and satellite transitions in the Q and P branches was studied in premixed stoichiometric methane-air and hydrogen-oxygen flames. Experimental signal traces are compared with expressions from a detailed theoretical treatment of the signal generation process using perturbation calculations. The theoretical approach consists in calculating the energy density in the signal field mode taking into account the frequency spread of the pump and probe beam radiation, collisional relaxation effects, and the polarization configuration of the incident beams. Relaxation times for population and orientation deduced from the fitting algorithm are in good agreement with DFWM line-shape studies [S. Williams et al., J. Chem. Phys. 104, 3947 (1996)]. It is shown that quantitative agreement with experimental data obtained for different polarization configurations of pump, probe, and signal photons can be achieved when appropriate time correlated interactions of pump and probe photons are taken into account. In addition, it is shown that due to the frequency spread of the employed laser pulses the different frequency components in the signal beam contribute with different amplitude to the oscillating and nonoscillating parts in the temporal development of the signal intensity depending on the relative strength of the simultaneously excited transitions.

Transition from superradiant free-polarization decay to subradiant photon-echo

Time-resolved degenerate four-wave mixing experiments on a multiple-quantum-well Bragg structure reveal a complex real-time pattern of the nonlinear optical response from the superradiant and the subradiant coupled exciton-photon modes. We find a free-polarization decay for the superradiant mode and a photon-echo from the subradiant modes. Rotation of the Bragg structure with respect to the incident laser beams implying a reduction of the effective quantum well separation results in a distinct change of the temporal behaviour. We estimate a value of less than 40 μeV for the nonradiative contribution to the homogeneous linewidth of free excitons in our GaAs samples.

Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale

The wavelength dependence of the third-order nonlinear optical susceptibilities, χ(3), of the Au:TiO2 composite films with Au concentration varying from 15% to 60% (volume fraction), was measured by a degenerate four-wave mixing (DFWM) technique using a probe laser with a pulse width of 200 fs. It was found that, with the wavelength of the probe laser close to the surface plasmon resonance (∼680 nm), both the χ(3) and the figure of merit, χ(3)/α (α is optical absorption coefficient) were significantly enhanced. The maximum value of the χ(3) was 6×10−7 esu and occurred at an Au concentration of about 38%. Femtosecond time-resolved DFWM measurements revealed that the response time of the optical nonlinearity in the Au:TiO2 films is extremely fast. The time-resolved DFWM results suggest that the main physical mechanism involved in the optical nonlinearity in Au:TiO2 films on the femtoseconds time scale is the interband electric–dipole transition, and the hot electron excitation only partially contributes to the χ(3) on the femtosecond time scale and it becomes dominant only in the picosecond region.

Ultrafast relaxation times of metalloporphyrins by time-resolved degenerate four-wave mixing with incoherent light

We present experimental results on the measurement of the population-relaxation times of the excited states of some metalloporphyrins such as zinc meso-tetra-phenylporphyrin (ZnmTPP), zinc meso-tetra (p-methoxyphenyl) tetrabenzporphyrin (ZnmpTBP), tetratollylporphyrin (TTP), cobalt tetratollylporphyrin (CoTTP) and nickel tetratollylporphyrin (NiTTP) with time-resolved degenerate four-wave mixing with the incoherent emission of a nanosecond pumped-dye laser. The experiments are carried out in the counterpropagating geometry (k4=k1+k2-k3), where k1 and k2 are counterpropagating to one another and k3 is at angle θ (<90° with respect to k1). Excited-state and ground-state relaxation times are calculated based on the theoretical formalism developed by Hiromi Okamoto [J. Opt. Soc. Am. B, 10, 2353, 1993]. The signals are recorded by delaying the probe beam (k3) for different fixed delays of the backward pump beam (k2). We observe strong signal at a second peak owing to the coherence of beams k2 and k3 for samples exhibiting excited-state absorption and a narrow peak corresponding to the coherence of beams k1 and k3 for samples that do not exhibit excited-state or reverse-saturable absorption. The nonlinear absorption is studied with the Z-scan technique. From the experimental data, we estimate the relaxation times of excited states.

Excited-state dynamics of thiophene thin films studied by time-resolved degenerate four-wave mixing

The resonant nonlinear optical response and singlet excited-state dynamics in the thin film of polydithieno (3,2-b; 2′, 3′-d) thiophene are studied by time-resolved degenerate four-wave mixing. Our experimental results, using &amp;lt;1 ps excitation at 635 nm, show that bimolecular decay via exciton–exciton annihilation dominates the temporal response at high intensities, thus decreasing the singlet lifetime. The measured rate constant of the singlet annihilation is k2=7.5×10−9 cm3/s. Estimates of the singlet-singlet annihilation, exciton diffusion coefficient, and hopping rate are obtained from the measurements.

Femtosecond Dynamics of Nonresonant Third-Order Optical Nonlinearity of 1-(3-thienyl)-3-(4-chlorophenyl)propene-1-one Crystal and Solution

For the crystal and solution of 1-(3-thienyl)-3-(4-chlorophenyl)propene-1-one (TCPP), which is transparent over the whole visible region, the nonresonant third-order nonlinear dynamics is investigated by time-resolved degenerate four-wave mixing spectroscopy. The temporal nonlinear behaviors of both crystal and solution exhibit the instantaneous responses during 80 fs excitation at around 625 nm. The third-order nonlinear susceptibilities are determined to be |χ(3)bbbb| = 7.1 ×10-13 esu for crystal and |χ (3)TC1111| = 7.1 ×10-14 esu at 1 mol/l for solution. This suggests that the TCPP crystal has a large value of χ(3)/ατ= 2.4 ×103 esu·cm·s-1 under the assumption of the nonlinear response time τ= 30 fs (absorption coefficient α= 0.01 cm-1), which is a parameter important for ultrafast optical control materials. The obtained |χ(3)bbbb| value satisfies an already known relationship between the second- and third-order susceptibilities.

Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors.

A direct optical measurement of electron drift mobility in multiple quantum well semiconductors is achieved by creating electron spin gratings in time-resolved degenerate four-wave mixing measurements. Grating decay rates are measured for spin and concentration gratings in a GaAs $/$AlGaAs sample at room temperature, giving an in-well electron diffusion coefficient ${D}_{e}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}127{\mathrm{cm}}^{2}/\mathrm{s}$ compared with an ambipolar coefficient ${D}_{a}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}13.3{\mathrm{cm}}^{2}/\mathrm{s}$.

Population gratings in degenerate four-wave mixing studies of a nickel dithiolene at 1064 nm

The nickel dithiolene complex Ni(S 2C 2PhBu) 2 has been studied using time-resolved degenerate four-wave mixing (DFWM) at 1064 nm. An analysis of the polarisation and temporal behaviour using the near-counter-propagating geometry shows that population gratings make a substantial contribution to the DFWM signals. These findings contrast with previous DFWM studies using a retro-reflection geometry which suggested that faster processes dominate. Experimental artefacts, inherent to the retro-reflection configuration, can account for this difference. Measurements of the orientational relaxation time in several solvents, and an estimated excited state lifetime in dichloromethane, are presented.

Preparation and non-linear optical properties of CdS quantum dots in Na2O-B2O3-SiO2 glasses by the sol-gel technique

Non-linear optical properties of CdS quantum dots embedded in the sol-gel derived Na2O-B2O3-SiO2x3 glass matrix have been studied using nanosecond degenerate four-wave mixing (DFWM), pump-probe experiments, and time-resolved subpicosecond DFWM measurements. The concentration of CdS microcrystallites was varied from 1.4 to 10.2 wt% while the particle size was controlled to be in the range of 3–6 nm in diameter so that the confinement effects can be realized. The third-order susceptibility, χ3, was determined to be of the order of 10−7-10−6 e.s.u. near the resonant wavelength between 450 and 470 nm by the nanosecond DFWM and pump-probe experiments, and of the order of 10−11-10−10 e.s.u. at the off-resonant wavelength, 580 nm, by a time-resolved DFWM measurement with 400 fs laser pulse. The decay time changed from 0.5 to 50 picoseconds as a function of the size, size distribution and number density of CdS microcrystallites in the glasses. Photodarkening reduced the optical non-linearity of the melt-quenched samples by a factor of ≈ 20, while it had no appreciable effect on that of the sol-gel derived samples.[/p]

Coherent dynamics of free and bound excitons in strained ZnSe epilayers

The coherent interaction of free and bound excitons in thin high-quality ZnSe layers is investigated by means of spectrally resolved as well as time-resolved degenerate four-wave mixing. In spectrally resolved data, signatures that are attributed to quantum beating occur whereas time-resolved data on the same sample exhibit effects arising from polarization interference. Additionally, for the first time interference has been observed between bound-exciton and biexciton contributions.

Picosecond degenerate four-wave mixing in colloidal solutions of gold nanoparticles at high repetition rates

Time-resolved degenerate four-wave mixing experiments on a colloidal solution of 50-nm gold particles in acetone, using a high-repetition-rate laser source, are presented. The signal is found to depend strongly on the repetition rate of the incident radiation and above a frequency of 300 kHz is impossible to measure.

Nonlinear optical responses of C 70-toluene solutions

The third-order optical nonlinear response in C 70-toluene solutions was studied by time-resolved degenerate four-wave mixing at 532 nm. Both the rise and decay time of the four-wave mixing signal were measured as a function of laser excitation energy. The observed decrease of the rise time as excitation intensity increases is attributed to the large singlet-singlet excited state absorption cross section. The decay time of the nonlinear response depended on the sample age and laser excitation and varied from 110 to 650 ps within the range of the various widely diverging published values.

Femtosecond Dynamics of Frenkel Excitons in Pseudoisocyanine J Aggregates

We report results of femtosecond pump-probe and degenerate four-wave mixing (DFWM) experiments in pseudoisocyanine J aggregates at 77 K. In the pump-probe experiments, the spectral oscillatory structure has been observed when the probe pulse precedes the pump pulse. This spectral oscillation is ascribed to the perturbed free induction decay of the J band. From the rise-up of the oscillation and results of DFWM experiments, the relaxation time is estimated from 300 to 600 fs. The time-resolved degenerate four-wave mixing spectroscopy is adopted to measure the coherent polarization decay in the J aggregates. The results clearly shows that the coherent polarization decay of the J band is ascribed to the free induction decay.

Degenerate Four-Wave Mixing as a Nonlinear Optical Probe of the Fullerenes

Abstract Time-resolved degenerate four-wave mixing experiments were conducted on pure C60 and chemically modified C60 using a picosecond tunable dye laser. Photopolymerization, oxygen doping or formation of charge transfer complexes in the ground or excited states were used to alter the electronic and chemical structure of C60. The third-order optical response for C60 was largely unaffected by photopolymerization or oxygen-doping whereas significant enhancements were observed for a C60:phenylenediamine derivative charge transfer complex and for a C60/substituted-polyphenylenevinylene composite. The chemical modification of C60 has a strong influence on the dynamics of the third-order response and gives rise to differing mechanisms.

Nonlinear optical responses of C 60-toluene solution

The third-order optical nonlinearities of C 60-toluene solution were studied by time-resolved degenerate four-wave mixing at 532 nm. The time response of the nonlinearities was measured for different polarization configurations to isolate the singlet excited state lifetime from the other relaxation components. The rise time of the four-wave mixing signal was found to shorten as the laser excitation energy increases. The rise time change is attributed to the larger singlet-singlet excited state absorption cross section. This assumption was supported by theoretical fits to the experimental data using rate equations and analysis, and by Z-scan measurements performed at the same wavelength.

Time-resolved DFWM, excite/probe and transient grating studies of InxGa1-xAs/GaAs superlattices

Low-temperature time-resolved degenerate four-wave mixing (DFWM), single-beam excite/probe and transient grating measurements have been performed on InxGa1-xAs/GaAs superlattices with thin ( approximately 6 nm) InxGa1-xAs wells. We find weak dephasing of heavy-hole (hh) excitons by acoustic phonons. The hh exciton homogeneous linewidth temperature coefficient is 1.9+or-1 mu eV K-1. The low-temperature hh exciton optical nonlinearity is successfully modelled in terms of exciton phase-space filling and exchange interactions in the hh exciton gas. From low-temperature transient grating measurements we find hh exciton in-plane mobilities as high as 6.7*104 cm2 V-1 s-1 and mobilities which are greater in superlattices with thinner barriers.

Ultrafast population relaxation by time-resolved degenerate four-wave mixing with incoherent light and analysis under breakdown of the two-level approximation

Time-resolved three-beam degenerate four-wave mixing with incoherent light for observation of population relaxation, originally proposed by Morita . [ J. Opt. Soc. Am. B4, 1269 ( 1987)] is examined both theoretically and experimentally. Theoretical calculation shows that a large part of the decaying signal in the time-resolved profile originates from the ground-state relaxation if the excited-state relaxation is faster than the ground-state relaxation. It is also shown that the use of a nonzero delay time between the k2 and k1 beams, in addition to that between the k3 and k1 beams (ks = k1 − k2 + k3, where k1–3 and ks are the wave vectors for the incident and the scattered beams, respectively), provides information on population relaxation, especially when the population-relaxation time is far longer than the correlation time of the incoherent light. These theoretical considerations are verified experimentally with the use of a triphenylmethane dye in solution.